Quantum Computation with Ions in Thermal Motion (original) (raw)

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Cold trapped ions as quantum information processors

Journal of Modern Optics, 2002

In this tutorial we review physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and confining of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travelling-wave and standing-wave configuration for dipole and quadrupole transitions. We review different types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb-Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on more advanced multi-qubit logic gates. We describe how quantum logic networks may be used for the synthesis of arbitrary pure quantum states. Finally, we discuss the speed of quantum gates and we also give some numerical estimations for them. A discussion of dynamics on off-resonant transitions associated with a qualitative estimation of the weak coupling regime and of the Lamb-Dicke regime is included in Appendix.

Tutorial review Cold trapped ions as quantum information processors

In this tutorial we review the physical implementation of quantum computing using a system of cold trapped ions. We discuss systematically all the aspects for making the implementation possible. Firstly, we go through the loading and con®ning of atomic ions in the linear Paul trap, then we describe the collective vibrational motion of trapped ions. Further, we discuss interactions of the ions with a laser beam. We treat the interactions in the travellingwave and standing-wave con®guration for dipole and quadrupole transitions. We review di erent types of laser cooling techniques associated with trapped ions. We address Doppler cooling, sideband cooling in and beyond the Lamb± Dicke limit, sympathetic cooling and laser cooling using electromagnetically induced transparency. After that we discuss the problem of state detection using the electron shelving method. Then quantum gates are described. We introduce single-qubit rotations, two-qubit controlled-NOT and multi-qubit controlled-NOT gates. We also comment on more advanced multiple-qubit logic gates. We describe how quantum logic networks may be used for the synthesis of arbitrary pure quantum states. Finally, we discuss the speed of quantum gates and we also give some numerical estimations for them. A discussion of dynamics on o -resonance transitions associated with a qualitative estimation of the weak-coupling regime is included in Appendix A and of the Lamb±Dicke regime in Appendix B.

A proposal of quantum logic gates using cold trapped ions in a cavity

Physics Letters A, 2002

We propose a scheme for implementation of logical gates in a trapped ion inside a high-Q cavity. The ion is simultaneously interacting with a (classical) laser field as well as with the (quantized) cavity field. We demonstrate that simply by tuning the ionic internal levels with the frequencies of the fields, it is possible to construct a controlled-NOT gate in a three step procedure, having the ion's internal levels as well as vibrational (motional) levels as qubits. The cavity field is used as an auxiliary qubit and basically remains in the vacuum state. 32.80.Lg, The coherent manipulation of simple quantum systems has become increasingly important for both the fundamental physics involved and prospective applications, especially on quantum information processing. Entanglement between two or more subsystems is normally required in order to have conditions for "quantum logical" operations to be performed. Two-level systems are natural candidates for building quantum bits (qubits), which are the elementary units for quantum information processing. We may mention single ions interacting with laser fields [1], atoms and field modes inside high-Q cavities [2], and molecules (via NMR) [3], as quantum subsystems which have shown themselves suitable for coherent manipulation. Regarding the atoms (or ions), both internal (electronic) as well as vibrational motion states may be readily used for performing quantum operations, e.g., a controlled-NOT gate , and a phase gate . It is therefore important to explore other combinations of (experimentally available) physical systems. An interesting set up is a single trapped ion inside a cavity. The quantized field couples to the oscillating ion so that we have three quantum subsystems: the center-of-mass ionic oscillation, the ion's internal degrees of freedom, and the cavity field mode. One of the advantages of such a system is the high degree of control one may achieve in trapped ions, allowing, for instance, long interaction times with the cavity field. A few papers may be found, in which it is investigated the influence of the field statistics on the ion dynamics [5,6], quantum state transfer [7], as well as a scheme to generate Bell-type states of the cavity-field and the vibrational motion . More recently, we may find propositions of other schemes involving the combination of trapped ions with cavity QED [9,10]. On the experimental side, a single trapped ion has been succesfully coupled to a cavity field , an important step towards the use of trapped ions for quantum computing and quantum communication purposes .

Trapped Ion Quantum Computing and the Principles of Logic

An experimental realization of quantum computers is composed of two or more calcium ions trapped in a magnetic quadripole. Information is transferred to and read from the ions by means of structured lasers that interact with the ions' vibration pattern, causing changes of energy distribution in their electronic structure. Departing from an initial state when the ions are cooled, the use of lasers modifies the internal state of one ion that is entangled with the others, then changing the collective states. In such quantum computers, some of the physically possible electronic states are avoided or not taken into consideration, to force the system to work as a binary device. In this essay, we discuss the dynamics that the ions could spontaneously display and its possible implications for the principles of computational logics.

Erratum to: “A proposal of quantum logic gates using cold trapped ions in a cavity”

Physics Letters A, 2002

We propose a scheme for implementation of logical gates in a trapped ion inside a high-Q cavity. The ion is simultaneously interacting with a (classical) laser field as well as with the (quantized) cavity field. We demonstrate that simply by tuning the ionic internal levels with the frequencies of the fields, it is possible to construct a controlled-NOT gate in a three step procedure, having the ion's internal levels as well as vibrational (motional) levels as qubits. The cavity field is used as an auxiliary qubit and basically remains in the vacuum state. 32.80.Lg, The coherent manipulation of simple quantum systems has become increasingly important for both the fundamental physics involved and prospective applications, especially on quantum information processing. Entanglement between two or more subsystems is normally required in order to have conditions for "quantum logical" operations to be performed. Two-level systems are natural candidates for building quantum bits (qubits), which are the elementary units for quantum information processing. We may mention single ions interacting with laser fields [1], atoms and field modes inside high-Q cavities [2], and molecules (via NMR) [3], as quantum subsystems which have shown themselves suitable for coherent manipulation. Regarding the atoms (or ions), both internal (electronic) as well as vibrational motion states may be readily used for performing quantum operations, e.g., a controlled-NOT gate , and a phase gate . It is therefore important to explore other combinations of (experimentally available) physical systems. An interesting set up is a single trapped ion inside a cavity. The quantized field couples to the oscillating ion so that we have three quantum subsystems: the center-of-mass ionic oscillation, the ion's internal degrees of freedom, and the cavity field mode. One of the advantages of such a system is the high degree of control one may achieve in trapped ions, allowing, for instance, long interaction times with the cavity field. A few papers may be found, in which it is investigated the influence of the field statistics on the ion dynamics [5,6], quantum state transfer [7], as well as a scheme to generate Bell-type states of the cavity-field and the vibrational motion . More recently, we may find propositions of other schemes involving the combination of trapped ions with cavity QED [9,10]. On the experimental side, a single trapped ion has been succesfully coupled to a cavity field , an important step towards the use of trapped ions for quantum computing and quantum communication purposes .

Light-Shift-Induced Quantum Gates for Ions in Thermal Motion

Physical Review Letters, 2001

An effective interaction between trapped ions in thermal motion can be generated by illuminating them simultaneously with a single laser resonant with the ionic carrier frequency. The ac Stark-shift induces simultaneous 'virtual' two-phonon transitions via several motional modes. Within a certain laser intensity range these transitions can interfere constructively, resulting in a relatively fast, heating-resistant two-qubit logic gate.

Quantum computing with trapped ions

Physics Reports, 2008

Quantum computers hold the promise to solve certain computational task much more efficiently than classical computers. We review the recent experimental advancements towards a quantum computer with trapped ions. In particular, various implementations of qubits, quantum gates and some key experiments are discussed. Furthermore, we review some implementations of quantum algorithms such as a deterministic teleportation of quantum information and an error correction scheme.

Quantum Computation with Trapped Ions in an Optical Cavity

Physical Review Letters, 2002

Two-qubit logical gates are proposed on the basis of two atoms trapped in a cavity setup. Losses in the interaction by spontaneous transitions are efficiently suppressed by employing adiabatic transitions and the Zeno effect. Dynamical and geometrical conditional phase gates are suggested. This method provides fidelity and a success rate of its gates very close to unity. Hence, it is suitable for performing quantum computation. * jip@mpq.mpg.de

A quantum information processor with trapped ions

New Journal of Physics, 2013

Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a small-scale quantum information processor based on a string of 40 Ca + ions confined in a macroscopic linear Paul trap. We review our set of operations which includes non-coherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire set of operations can be used to facilitate the implementation of algorithms by examples of the quantum Fourier transform and the quantum order finding algorithm.